The arithmetic mean of the first 100 natural numbers is 50.5.
Understanding Arithmetic Mean
The arithmetic mean, often referred to as the average, is calculated by summing a set of numbers and then dividing by the count of those numbers. In this case, we're dealing with the first 100 natural numbers (1, 2, 3,...100).
Calculating the Arithmetic Mean
There are two primary ways to calculate this:
- Direct Calculation: Sum all the numbers from 1 to 100, and then divide by 100.
- Using the Formula: For the sum of the first 'n' natural numbers, we can use the formula:
Sum = n(n+1) / 2. Then, to find the arithmetic mean, we divide this sum by 'n'.
Applying the Formula
- n = 100 (number of natural numbers)
- Sum = 100 (100 + 1) / 2 = 100 101 / 2 = 5050
- Arithmetic Mean = Sum / n = 5050 / 100 = 50.5
Therefore, the arithmetic mean of the first 100 natural numbers is indeed 50.5.
